Yettaw, a Vietnam war veteran who suffers from epilepsy, was sentenced to seven years of hard labour and imprisonment.
Aung San Suu Kyi was given three years hard labour and imprisonment, but that sentence was commuted to 18 months house arrest on the orders of Senior General Than Shwe, the head of Myanmar's military government.
The 64-year-old opposition leader, who has spent 14 of the last 20 years in jail or under house arrest, has described the verdict as "totally unfair", according to one of her lawyers who say she plans to appeal.
Speaking to reporters in New York, Sawers sought to explain why an initial US-drafted text was watered down.
"I think we all know that different members of the Security Council have different views on the situation there and that the strong views in various Western capitals are not entirely shared in countries elsewhere," he said.
A tougher US-drafted statement, which would have strongly condemned Aung San Suu Kyi's conviction ran into opposition from China, a key ally of Myanmar, as well as from Russia, Vietnam and Libya.
China voiced the loudest concern to the initial statement, calling for Myanmar's judicial sovereignty to be respected and warned international powers to stay out of the country's internal affairs.
Beijing has long adopted a policy of non-interference in the internal affairs of Myanmar and has helped keep the impoverished nation economically afloat through trade ties, arms sales, and by shielding it from UN sanctions over rights abuses.
The text approved on Thursday affirmed the council's "commitment to the sovereignty and territorial integrity of Myanmar" and reiterated that "the future of Myanmar lies in the hands of all its people".
It also noted the government's decision to reduce Aung San Suu Kyi's sentence and urged the government "to take further measures to create the necessary conditions for a genuine dialogue with Daw Aung San Suu Kyi and all concerned parties and ethnic groups in order to achieve an inclusive national reconciliation".